If $Gamma$ is a discrete subgroup of $PSL(3,Bbb{C})$, it is determined the equicontinuity region $Eq(Gamma)$ of the natural action of $Gamma$ on $Bbb{P}^2_Bbb{C}$. It is also proved that the action restricted to $Eq(Gamma)$ is discontinuous, and $Eq(Gamma)$ agrees with the discontinuity set in the sense of Kulkarni whenever the limit set of $Gamma$ in the sense of Kulkarni, $Lambda(Gamma)$, contains at least three lines in general position. Under some additional hypothesis, it turns out to be the largest open set on which $Gamma$ acts discontinuously. Moreover, if $Lambda(Gamma)$ contains at least four complex lines and $Gamma$ acts on $Bbb{P}^2_Bbb{C}$ without fixed points nor invariant lines, then each connected component of $Eq(Gamma)$ is a holomorphy domain and a complete Kobayashi hyperbolic space.
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